Vincent Trocheck scored his 200th NHL goal, Chris Kreider scored short-handed, Mika Zibanejad had three assists, and Adam Edstrom got his first of the season for the Rangers (8-2-1), who have won two games in a row and three of four.
"I thought it was good," Rangers coach Peter Laviolette said. "Giving up the goal late in the [second] period, that was tough. That brings the game closer. But then I really liked us going back out for the third period. So, overall, I was pretty happy with all three periods. I thought 5-on-5, power play and penalty kill was all pretty good."
Ilya Sorokin made 35 saves, and Casey Cizikas and Brock Nelson scored for the Islanders (4-6-2), who have lost four of five all in regulation.
The Islanders went 0-for-5 on the power play and gave up the short-handed goal to Kreider at 3:44 of the first period.
"We have five power plays, we'd like to cash in on one," Islanders forward Anders Lee said. "There's nothing more to say about that. "
The Rangers came into Sunday with new forward lines and defense pairs, including Jimmy Vesey making his season debut after missing the first 10 games on long-term injured reserve for a lower-body injury.
The new look up front and on the back end was a reaction to how Laviolette felt they were playing in their recent games; under attack too often, unable to get the puck out of the zone or sustain pressure in the offensive zone.
The Rangers won 2-1 against the Ottawa Senators on Friday even though they were outshot 41-18, including 20-5 in the third period. They lost 5-3 to the Washington Capitals on Tuesday, getting outshot 46-19.
Zibanejad, who played on a line with Panarin and Alexis Lafreniere after playing with Kreider and Reilly Smith for the first 10 games, said the changes, especially coming off a win, got the team's attention.
"But at the same time, I can look at in a way where we have a record of 7-2-1 and we think we can play better," Zibanejad said. "I would say that's a good problem to have. And we do it. We come out here and I think we played one of our most solid games all season. That shows what kind of team we have and what kind of group we have in here."
Kreider gave the Rangers a 1-0 lead off a rush with Zibanejad that started with Noah Dobson's giveaway in the neutral zone. They passed the puck back and forth before Zibanejad found Kreider below the right circle for a one-timer that got behind Sorokin.
"He made a great play to me, and he just got open and he was ready for a pass back and I thought the lane was pretty open," Zibanejad said. "It was a good start for us."